 
 
 
11.9.6  Inverse of a matrix in ℤ/pℤ
In Xcas mode, Inverse is simply the inert form of
inverse; namely, it gives the inverse of a matrix without
evaluating it. (See Section 15.1.2.)
In Maple mode, the Inverse command
can additionally be used in conjunction with mod to
find the inverse of a matrix whose elements are in
ℤ/pℤ.
- 
In Maple mode, Inverse takes
A, a matrix with elements in ℤ/pℤ.
- Inverse(A) returns the inverse of A.
Example
Input in Xcas mode:
| Inverse([[1,2,9] mod 13,[3,10,0] mod 13,[3,11,1] mod13]) | 
|  | | | inverse | ⎛ ⎜
 ⎜
 ⎜
 ⎜
 ⎜
 ⎝
 |  | | ⎡ ⎢
 ⎢
 ⎢
 ⎢
 ⎢
 ⎣
 | | 1%13 | 2%13 |  |  | 3%13 |  | 0%13 |  | 3%13 |  | 1%13 | 
 | ⎤ ⎥
 ⎥
 ⎥
 ⎥
 ⎥
 ⎦
 | 
 |  | ⎞ ⎟
 ⎟
 ⎟
 ⎟
 ⎟
 ⎠
 | 
 |  |  |  |  |  |  |  |  |  |  | 
 | 
To get the actual inverse, enter:
|  | | |  | | ⎡ ⎢
 ⎢
 ⎢
 ⎢
 ⎢
 ⎣
 |  | ⎤ ⎥
 ⎥
 ⎥
 ⎥
 ⎥
 ⎦
 | 
 | 
 |  |  |  |  |  |  |  |  |  |  | 
 | 
which is the inverse of A=[[1,2,9],[3,10,0],[3,11,1]] in ℤ/13ℤ.
Input in Maple mode:
| Inverse([[1,2,9],[3,10,0],[3,11,1]]) mod 13 | 
 
 
